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Re: Anomaly? or at least a surprise.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg90284] Re: Anomaly? or at least a surprise.
*From*: "David Park" <djmpark at comcast.net>
*Date*: Fri, 4 Jul 2008 03:59:26 -0400 (EDT)
*References*: <g4i942$3cr$1@smc.vnet.net>
First notice that
D[ArcTan[x]] gives
ArcTan[x]
So
Plot[D[ArcTan[x]], {x, -10, 10}, PlotRange -> Full]
is just a plot of ArcTan[x], if that is what you wanted. You might as well
just have used ArcTan[x]. But
Plot[D[ArcTan[x], x], {x, -10, 10}, PlotRange -> Full]
is evaluated by substituting numerical values of x into the plot expression.
For example, when Mathematica is evaluating for x = .5, say, it tries to
evaluate:
D[ArcTan[.5], .5]
which is nonsense because the second argument is not a symbolic variable
and, even if it was, the first argument does not contain a symbolic variable
but is evaluated to a number.
But the plot statement will work if you Evaluate the plotting expression.
Plot[D[ArcTan[x], x] // Evaluate, {x, -10, 10}, PlotRange -> Full]
Which all leads to a useful, but certainly not ironclad, rule. Don't cram a
lot of calculation into plotting expressions. Look at them first, outside
the plotting statement, and make certain you know what they are. Then you
might even define a function for them and put that into the plotting
statement.
f[x_] = D[ArcTan[x], x]
Plot[f[x], {x, -10, 10}, PlotRange -> Full]
Or, in this case, there is even a simpler solution:
Plot[ArcTan'[x], {x, -10, 10}, PlotRange -> Full]
--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
"Steve Gray" <stevebg at roadrunner.com> wrote in message
news:g4i942$3cr$1 at smc.vnet.net...
> Doing D[ArcTan[x], x] gives 1/(x^2+1) as expected.
> Doing Plot[D[ArcTan[x]],{x,-10,10},PlotRange->Full] with no variable
> to differentiate by gives a correct plot (!) This is surprising - Help
> says nothing about leaving out the independent variable even when the
> function is of only one variable. Now, doing
> Plot[D[ArcTan[x], x], {x, -10, 10}, PlotRange -> Full]
> gives error messages such as
>
> General::ivar: -9.18326 is not a valid variable. >>
> General::ivar: -9.59143 is not a valid variable. >>, etc.
>
> I thought that D[ArcTan[x], x] and 1/(x^2+1) should behave identically
> in the Plot statement.
>
> Is this behavior something I should know? Thank you.
>
> Steve Gray
>
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